20 ideas
13939 | No possible evidence could decide the reality of numbers, so it is a pseudo-question [Carnap] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
13936 | Questions about numbers are answered by analysis, and are analytic, and hence logically true [Carnap] |
8748 | Logical positivists incorporated geometry into logicism, saying axioms are just definitions [Carnap, by Shapiro] |
8960 | Internal questions about abstractions are trivial, and external ones deeply problematic [Carnap, by Szabó] |
13933 | Existence questions are 'internal' (within a framework) or 'external' (concerning the whole framework) [Carnap] |
13934 | To be 'real' is to be an element of a system, so we cannot ask reality questions about the system itself [Carnap] |
13938 | A linguistic framework involves commitment to entities, so only commitment to the framework is in question [Carnap] |
13935 | We only accept 'things' within a language with formation, testing and acceptance rules [Carnap] |
13932 | Empiricists tend to reject abstract entities, and to feel sympathy with nominalism [Carnap] |
13937 | New linguistic claims about entities are not true or false, but just expedient, fruitful or successful [Carnap] |
13940 | All linguistic forms in science are merely judged by their efficiency as instruments [Carnap] |
7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |